85.64.6 problem 1 (f)

Internal problem ID [22873]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 4. Linear differential equations. A Exercises at page 213
Problem number : 1 (f)
Date solved : Thursday, October 02, 2025 at 09:16:02 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }+y&=16 \sin \left (\ln \left (x \right )\right ) \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 92

ode:=x^2*diff(diff(y(x),x),x)+y(x) = 16*sin(ln(x)); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\sqrt {x}\, \left (32 \sqrt {3}\, \sin \left (\frac {\sqrt {3}\, \ln \left (x \right )}{2}\right ) \int \frac {\cos \left (\frac {\sqrt {3}\, \ln \left (x \right )}{2}\right ) \sin \left (\ln \left (x \right )\right )}{x^{{3}/{2}}}d x -32 \sqrt {3}\, \cos \left (\frac {\sqrt {3}\, \ln \left (x \right )}{2}\right ) \int \frac {\sin \left (\frac {\sqrt {3}\, \ln \left (x \right )}{2}\right ) \sin \left (\ln \left (x \right )\right )}{x^{{3}/{2}}}d x +3 c_2 \sin \left (\frac {\sqrt {3}\, \ln \left (x \right )}{2}\right )+3 c_1 \cos \left (\frac {\sqrt {3}\, \ln \left (x \right )}{2}\right )\right )}{3} \]

✓ Mathematica. Time used: 0.401 (sec). Leaf size: 48

ode=x^2*D[y[x],{x,2}]+y[x]==16*Sin[ Log[x] ]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 16 \cos (\log (x))+\sqrt {x} \left (c_1 \cos \left (\frac {1}{2} \sqrt {3} \log (x)\right )+c_2 \sin \left (\frac {1}{2} \sqrt {3} \log (x)\right )\right ) \end{align*}

✓ Sympy. Time used: 0.184 (sec). Leaf size: 46

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) + y(x) - 16*sin(log(x)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} \sqrt {x} \sin {\left (\frac {\sqrt {3} \log {\left (x \right )}}{2} \right )} + C_{2} \sqrt {x} \cos {\left (\frac {\sqrt {3} \log {\left (x \right )}}{2} \right )} + 16 \cos {\left (\log {\left (x \right )} \right )} \]